The most important processes in the channel of catalytic monolith converter of exhaust gases are convection of gas, heat and mass transfer between the flowing gas and washcoat on the channel walls, internal diffusion and catalytic reactions in the porous washcoat, heat and mass accumulation, and heat conduction. These processes take place on several different length-scales – monolith length and diameter are on the order of 10 cm, the channel diameter is approx. 1 mm, the porous catalytic washcoat layer usually exhibits thickness on the order of 10-100 µm, typical diameter of the particles forming the supporting material (e.g. gamma-Al2O3) is on the order of 1 µm, meso- and micro-pores of the supporting material have diameter on the order of 1-10 nm, the size of active catalytic sites is in nanometres, and the reacting molecules size is in the order of angstroms.

In this contribution development of a multi-scale model of catalytic monolith for conversion of exhaust gases is discussed. Two models of different hierarchical levels are presented:

1. Effective, full-scale model of catalytic monolith, spatially 1D distributed, based on solution of mass and heat transport in monolith channel. In the spatially 1D model of the monolith channel, no transverse concentration gradients inside the catalytic washcoat layer are considered, i.e. the influence of internal diffusion is neglected or just included in the employed reaction-kinetic parameters [1,2]. To overcome this limitation, the effectiveness-factor concept can be used in a limited extent. Despite the drawbacks coming from the fact that internal diffusion effects are neglected or implicitly included in the reaction kinetics, the 1D plug-flow model is extensively used in industry, due to reasonable combination of physical reliability and short computation times [2].

2. Detailed, spatially 3D model of small section of active catalytic layer (monolith washcoat), based on digital reconstruction of porous media and solution of reaction-transport processes. The structure of porous catalyst support is controlled in the course of washcoat preparation on two levels: (i) the level of macro-pores, influenced by mixing of wet supporting material particles with different sizes followed by specific thermal treatment, and (ii) the level of meso-/micro-pores, determined by the internal nano-structure of the used materials (e.g., alumina, zeolites) and sizes of noble metal crystallites. Information about the porous structure (pore size distribution, typical sizes of particles, etc.) on the micro- and nano-scale levels can be obtained from scanning electron microscopy (SEM), transmission electron microscopy (TEM) or other high-resolution imaging techniques in combination with mercury porosimetry and BET adsorption isotherm data. This information can be used in computer reconstruction of porous catalytic medium. In the reconstructed catalyst, transport (diffusion, permeation, heat conduction) and combined reaction-transport processes can be simulated on detailed level [3-6].

The local reaction rates and effectiveness factors, calculated by the detailed model of catalytic washcoat in dependence on gas components concentrations, temperature and the properties of porous structure (cf., e.g., [3]) can be used as input values for simulations at the larger scale in the effective, spatially 1D model of monolith channel. This coupling can improve the accuracy of the predicted behaviour of catalytic monolith and reflect the influence of the catalyst layer properties on the performance of entire monolith reactor [7].

References

[1] Kočí P., M. Kubíček, M. Marek: Modelling of TWC monolith converters with microkinetics and diffusion in the washcoat, Ind. Eng. Chem. Res. 43, (2004), 4503.

[2] Güthenke A., Chatterjee D., Weibel M., Waldbüßer N., Kočí P., Marek M., Kubíček M.: Development and Application of a Model for a NOx Storage and Reduction Catalyst, Chemical Engineering Science 62 (2007) 5357.

[3] Kočí P., F. Štěpánek, M. Kubíček, M. Marek: Meso-scale modelling of CO oxidation in digitally reconstructed porous Pt/gamma-Al2O3 catalyst, Chemical Engineering Science 61, (2006), 3240.

[4] Kočí P., F. Štěpánek, M. Kubíček, M. Marek: Modelling of micro/nano-scale concentration and temperature gradients in porous supported catalysts, Chemical Engineering Science 62 (2007) 5380.

[5] Kočí P., F. Štěpánek, M. Kubíček, M. Marek: Pore-scale modelling of non-isothermal reaction

phenomena in digitally reconstructed porous catalyst, Molecular Simulation 33 (2007) 369.

[6] Kosek J., F. Štěpánek, M. Marek. Modelling of transport and transformation processes in porous and multiphase bodies. Advances in Chemical Engineering 30 (2005) 137.

[7] http://www.vscht.cz/monolith

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